In previous work with spatial models of biological processes [1]}, TDA has been applied to test for spatial randomness [2]}, automatically detect zebra-fish patterns [3]}, characterise immune cell infiltration by changes in a chemotaxis parameter [4]}, and cluster parameter regimes for angiogenesis [5]}. Now we wish to address the inverse problem of recovering model parameters given some observed data, in the Bayesian formalism. ABC enables us to perform parameter inference in a statistical model on the basis of data summaries, even when there is no clear way to define a likelihood function for the model. One key challenge in ABC is the choice of summary statistic, as the statistic must capture the relevant information about the model parameters in the data to allow the parameters to be learnt. Here we show that TDA provides informative data summaries that enable parameter inference to be performed successfully in a spatial model. In particular, we consider as a case study the Anderson-Chaplain model of angiogenesis [6]}.
